One concept alot of people can't seem to grasp is parallax. While it's not something that the majority of people have to deal with for short range stuff, like hunting, it is something that can be annoying and painful to people that shoot rimfire or long range.
Parallax is the difference between the focal planes of the target and your scope's reticle. When the scope's reticle is not in the same focal depth the reticle will appear to move faster than the target with any movement of your head, and visa versa depending on which depth is nearer to your eye. This induces error and can open up groups considerably. You will also find it difficult to focus on the reticle and the target at the same time which causes significant amounts of eye strain.
It's best understood visually.
Put one finger in front of you like you would to represent the number one about 6" in front of your face. Now, extend your other arm to full extension and put up your finger in the same manner. Line both fingers up; you may close one eye if you have trouble doing so.
Without moving your hands, move your head left to right. Notice how the finger nearest to you "moves" alot while the finger furthest from you seems to not "move" at all. This is an optical illusion due to parallax.
Imagine the near finger is the scope's reticle and the rear finger is the target, voila you now understand what is going on visually.
Parallax in a Scope
Here's two pictures of my scope set to 5.5x with the parallax adjustment bottomed out. The target is very near, approx 7 yards away.
This is the reticle in view through my Olympus camera. The focal depth is approximately 2 meters.
This is the "target" in view through my Olympus camera. The focal depth is only 0.2 meters.
At this range the reticle's depth is 10 times the depth of the target. It is impossible for the human eye to focus on both the reticle and the target at this distance. With these parallax settings I find that the target must be beyond 25 yards to start to gain clarity, with full clarity by 50 yards. With most centerfire scopes, like my Nightforce NXS, the focal range generally starts around 40 - 50 yards.
So what can you do to fix parallax errors?
Parallax is entirely equipment related in regards to eliminating it, however, if you are dealing with parallax in your current configuration, you ABSOLUTELY cannot break your cheek weld. Even small movements behind the scope will cause shift in the reticle and target view.
In regards to equipment, most manufacturers design scopes to operate well within a "normalized" range. For non-adjustable centerfire scopes this generally is between 100 - 200 yards, so the vast majority of shooters will never run into errors since they make most of their shots at this range. Rimfire scopes are usually specified with a 50 - 75 yard parallax setting, since the vast majority of rimfire shooters do so at close range.
This essentially means that for shooting at 50 yards a scope with a fixed focal depth of 100 - 200 yards will give parallax and significant eye strain.
Many scopes are available with adjustable objectives (Leupold VX-II for example) and side mounted parallax adjustment (pictured above) that allows you to adjust the parallax to the specific range. The above Nightforce for example gives excellent results anywhere from 50 yards to 1000+ yards via the adjustment.
This allows the user to use an adjustable parallax scope on anything from a .22 LR to a .243 Win to a .50 BMG at a wide range of distances.
"As a scope feature, all of my future scopes will have adjustable parallax."